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%I #4 Mar 31 2012 13:21:17
%S 0,1,3,2,7,8,6,4,5,17,18,20,21,22,16,19,14,10,9,15,11,12,13,45,46,48,
%T 49,50,54,55,57,58,59,61,62,63,64,44,47,53,56,60,42,51,38,26,27,37,25,
%U 23,24,43,52,39,29,28,40,30,31,32,41,33,34,35,36,129,130,132,133,134
%N Signature permutation of a Catalan bijection: The inverse of A154451.
%C This automorphism of rooted plane binary trees switches the two descendant trees for every other vertex as it descends along the 111... ray, starting swapping already at the root. Specifically, *A154452 = psi(A154442), where the isomorphism psi is given in A153141 (see further comments there).
%H A. Karttunen, <a href="/A154452/b154452.txt">Table of n, a(n) for n = 0..2055</a>
%H <a href="/index/Per#IntegerPermutationCatAuto">Index entries for signature-permutations of Catalan automorphisms</a>
%o (Scheme function, destructive implementation of this automorphism acting on S-expressions:) (define (*A154452! s) (cond ((pair? s) (*A069770! s) (*A154450! (cdr s)))) s)
%Y Inverse: A154451. a(n) = A069767(A154454(n)) = A057163(A154456(A057163(n))). Cf. A069770, A154450.
%K nonn
%O 0,3
%A _Antti Karttunen_, Jan 17 2009
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